with \(E_0(k)=A k^{4} \exp \left(-\left(k / k_{0}\right)^{2}\right)\) , and \(\Psi (k)\)  coming from a uniform distribution between 0 and 1 for each wavenumber (\(\Psi (k)=\mathcal {U}(0,1)\) ). The constants \(A\)  and \(k_0\)  are the same as in [1]}. Selecting the initial conditions in this manner results in training and testing datasets with a variety of different initial energies.
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